2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/142879To any weighted graph of first Betti number b is naturally associated a lattice of dimension b, definite in a similar way that the jacobian for a Riemann surface. This class of lattices generated by graphs is particularly interesting. We show here an upperbound of the Hermite invariant of such a lattice according to b whose order is ln b. This order is optimal : it is realized by the Hermite invariant of the jacobian of a systolicly economic graph.9 pagesCombinatoricsMetric GeometryNumber Theory05C35, 05C38, 11H31text